As discussed in Section , our formulation of the system identification problem in Section  and the corresponding solution method in Sections  and  allow for significantly lower data requirements and less stringent limitation on the network structure than other methods (e.g., in [1]} and [2]}) that are developed to construct a sparse system model. We illustrate our proposed sparse identification approach with two examples that could not have been computed with the methods in [1]} and [2]}.
In Section REF , we identify the structure of an unknown system without measuring the full state vector, where the identification is based on measurements with different sampling rates. In Section REF , we train a network to approximate the error in the first-principle model without the requirement that the network model is linear in its parameters. We show that sparsification can simplify a network model while at the same time improve its accuracy by reducing overfitting.
